We report on a measurement of the inclusive jet production cross section as a function of the jet transverse momentum in pp collisions at s√=1.96 TeV using data collected with the upgraded Collider Detector at Fermilab in run II, corresponding to an integrated luminosity of 385 pb−1. The measurement is carried out for jets with rapidity 0.1<|yjet|<0.7 and transverse momentum in the range 54<pjetT<700 GeV/c. Next-to-leading order perturbative QCD predictions are in good agreement with the measured cross section after the necessary nonperturbative parton-to-hadron corrections are included.